Try entering different sets of numbers in the number pyramids. How does the total at the top change?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Work out how to light up the single light. What's the rule?

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?